The present invention relates to the field of medical devices to treat neurological disorders of the brain.
Complex dynamic systems that are open to energy/mass and/or information exchanges with their environment typically display emergent properties of self organization (SO)—patterns or behaviors ascribable to the collective ensemble but not particularly in the individual components. A class of SO behavior, termed self-organized criticality (SOC), can be sustained for certain ranges of system parameters in which energy fluctuations lose their characteristic amplitude and time scale, thus displaying self-similar events on a wide range of scales. In an SOC state, the system slowly accumulates some form of energy/mass and/or information that makes it prone to a fast “catastrophic” event. A small perturbation can be sufficient to start the event, which in turn can unleash a domino effect. Thus, the dramatic qualitative changes appear to come abruptly, can spread, and often occur in clusters. While this chain of events naturally seeks a more stable configuration, the “accumulating” variable is destabilizing and thus the cycle self-perpetuates. The critical state is globally attractive and robust: in a subcritical state there would be room for “tension” to build up towards the critical state, whereas in a supercritical state, a very large event would release tension back down to the critical state.
Because replicas of the above phenomenon exist at all amplitudes and time scales, a hallmark of SOC is a power-law distribution of frequency vs. the size of events (and event durations, and possibly inter-event intervals). The probability distribution P(E) of an event of size E follows the shape of 1/Eα, so that if one plots log(P(E)) vs. log(E), a straight line with slope-α results. Such plots have been displayed in disparate contexts as Zipf and Pareto distributions, but they arguably manifest a common trait of SOC in which a complex system yields frequent small events, rare big events, and an orderly distribution of everything in between. Examples are ubiquitous, including the spatial distribution of galaxies, the distribution of wealth in nations, the prices on commodities markets, the population of cities, the transient of blackouts in power grids, the magnitude and temporal statistics of earthquakes, the behavior of snow and granule avalanches, the spread of forest fires, the activity of volcanoes, the water volume and times of rainfall, the vortices of turbulent flow, the frequency of use of a few common words, and the number of visitors attracted to Web sites, ranked by popularity.
There is strong evidence that seizures in the human brain have similarities to and features in common with such critical systems-like behavior (e.g., systems behavior comparable to SOC). See G. A. Worrell, S. D. Cranstoun, B. Litt, and J. Echauz, “Evidence for Self-Organized Criticality in Human Epileptic Hippocampus,” NeuroReport, vol. 13, no. 16, pp. 1-5, 2002. Any brain learns and therefore self-organizes. The epileptic brain, however, appears to self-organize in the critical state, with seizures, seizure-like bursts, sharp waves, and spikes being the obvious multiple-size energy-dissipating events describable by the SOC theory.
The evidence of these findings in clinical observations is well appreciated, but not well described. For example, it is well known that individuals with epilepsy often display a type of conservation of dissipated “energy” in seizures, roughly measured by the amount of brain involved, the duration and severity of the events. This characteristic of an individual's seizures is also measured roughly by quantities such as the severity×duration×frequency of seizures.
There are many factors that can alter these individual variables, such as alterations in seizure medications, changes in seizure precipitants, underlying medical condition, and other factors. When a change in one of these factors takes place, affecting something such as seizure frequency, there is often a compensatory change in another parameter, such as amount of brain involved (e.g. simple partial, vs. complex partial, vs. secondarily generalized, in the case of partial onset seizures), duration or severity. As an example, a change in medications may convert a patient with a stable pattern of 4 complex partial seizures per month into 1 generalized convulsive seizure during the same time period, of the duration and severity roughly, averaged over time, to dissipate the same “energy” as the 4 milder seizures. Similarly, a patient with intermittent convulsions might be converted into much more frequent simple partial events. In the case of primarily generalized seizures, it may be that generalized convulsive events may be transformed into much less frequent absence, myoclonic or much smaller events. Again, these are inexact phenomena, and the above examples are provided more to illustrate these relationships rather than to describe an exact mathematical property of epilepsy.
In computer models of locally-coupled integrate-and-fire oscillator networks, “avalanches” in the number of firing oscillators have been observed with a lack of characteristic size for a certain range of network and driving function parameters. In an investigation of the pathological energy fluctuations in hippocampi of 7 patients with medication-resistant temporal lobe epilepsy, it was found that the frequency of occurrence of discharges of size E scaled as E−δ, and the frequency of occurrence of periods of size T between events scaled as T−γ, over a range a decade and a half or more in size. This finding is consistent with the electrographic occurrence of numerous small epileptiform events in a given patient, the clinical observation of less numerous severe or grand-mal seizures in the same patient, and the tendency for seizures to occur in flurries. Furthermore, it was found that the scaling behavior itself (as characterized, e.g., by the slope parameter in log-log axes) may drift from one “constant” during an interictal state, to another and into a loss of linearity during a preictal state (e.g., 1 hour before catastrophic ictus). Such changes in scaling exponent are also observed in the integrate-and-fire oscillators model as a function of system parameters. These results demonstrated the presence of SOC-like scaling over a range more than a decade wide in the human epileptic brain.
It is desirable to expand on these findings and provide ways to use a measure of critical systems-like behavior to manage seizures in a patient.